Characteristics of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, as there are no restrictions on the values that x can take.

Front

What is the range of a linear function?

Back

The range of a linear function is also all real numbers, as the function can take any value for y.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases. For linear functions, this occurs when the slope is positive.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, y decreases. For linear functions, this occurs when the slope is negative.

Front

What is the significance of a zero slope?

Back

A zero slope indicates that the function is constant; it does not change as x changes, resulting in a horizontal line.

Front

How can you determine where a linear function is positive?

Back

A linear function is positive where the output (y) is greater than zero. This can be found by solving the inequality mx + b > 0.